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%I #15 Oct 28 2022 08:16:56
%S 1,-2,0,-8,-10,-44,-104,-352,-1066,-3564,-11856,-40720,-141284,
%T -497464,-1768368,-6343808,-22926426,-83402956,-305142432,-1122083312,
%U -4144811244,-15372407464,-57222156528,-213709942208,-800563540356,-3007228179064,-11325019883616
%N Expansion of sqrt(1-4x)/(1-2x^2).
%F a(n) = Sum_{k=0..floor(n/2)} binomial(2(n-2k), n-2k)/(1-2(n-2k))*2^k.
%F Recurrence: n*a(n) +2*(-2*n+3)*a(n-1) -2*n*a(n-2) +4*(2*n-3)*a(n-3) = 0. - _R. J. Mathar_, Feb 20 2015
%p with(FormalPowerSeries): # requires Maple 2022
%p rec:=subs(n=n-1,FindRE(sqrt(1-4*x)/(1-2*x^2),x,r(n))); # yields Mathar's recurrence
%p a:=gfun:-rectoproc({rec, r(0)=1, r(1)=-2, r(2)=0}, r(n), remember);
%p seq(a(n), n=0..20); # _Georg Fischer_, Oct 28 2022
%t CoefficientList[Series[Sqrt[1-4x]/(1-2x^2),{x,0,30}],x] (* _Harvey P. Dale_, Mar 31 2015 *)
%Y Cf. A106192.
%K easy,sign
%O 0,2
%A _Paul Barry_, Apr 24 2005
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